EnergyScale

class madspace.EnergyScale(*args, **kwargs)

Bases: FunctionGenerator

Renormalization and factorization scales for an event.

Computes the renormalization scale and the two factorization scales from the event momenta. Each can be fixed to a constant or set to a dynamical choice (Sec. 3.2.6 of [1], matching the choices in [2]):

\[\mu = \sum_i m_i, \qquad \mu = E_\mathrm{T} = \sum_i \frac{E_i\,p_{\mathrm{T},i}}{|\vec p_i|},\]

\[\mu = H_\mathrm{T} = \sum_i \sqrt{m_i^2 + p_{\mathrm{T},i}^2},\]

with DynamicalScaleType selecting \(E_\mathrm{T}\) (transverse_energy), \(H_\mathrm{T}\) (transverse_mass), \(H_\mathrm{T}/2\) (half_transverse_mass) or \(\sqrt{\hat s}\) (partonic_energy). The dynamical scale is multiplied by scale_factor, e.g. \(H_\mathrm{T}/4\) is half_transverse_mass with scale_factor = 0.5. A CustomFunction of type CustomFunction::scale replaces the dynamical choice, like user_dynamical_scale in MadGraph5.

batch is the leading batch dimension.

Arguments

• momenta – float, shape (batch, particle_count, 4) – the event momenta.

Returns

• ren_scale – float, shape (batch,) – renormalization scale.

• fact_scale1 – float, shape (batch,) – factorization scale for the first beam.

• fact_scale2 – float, shape (batch,) – factorization scale for the second beam.

References

• [1] T. Heimel, O. Mattelaer, R. Winterhalder, “MadSpace”, https://arxiv.org/abs/2602.06895 (Sec. 3.2.6)

• [2] V. Hirschi, O. Mattelaer, “Automated event generation for loop-induced processes”, https://arxiv.org/abs/1507.00020

Overloaded function.

1. __init__(self: madspace._madspace_py.EnergyScale, particle_count: typing.SupportsInt) -> None

Dynamical half_transverse_mass for all three scales.

Parameters:

particle_count – Number of external particles.

2. __init__(self: madspace._madspace_py.EnergyScale, particle_count: typing.SupportsInt, type: madspace._madspace_py.EnergyScale.DynamicalScaleType) -> None

Dynamical scale of type type for all three scales.

Parameters:

• particle_count – Number of external particles.

• type – The dynamical scale choice.

3. __init__(self: madspace._madspace_py.EnergyScale, particle_count: typing.SupportsInt, fixed_scale: typing.SupportsFloat) -> None

A single fixed value for all three scales.

Parameters:

• particle_count – Number of external particles.

• fixed_scale – The constant scale value.

4. __init__(self: madspace._madspace_py.EnergyScale, particle_count: typing.SupportsInt, dynamical_scale_type: madspace._madspace_py.EnergyScale.DynamicalScaleType, ren_scale_fixed: bool, fact_scale_fixed: bool, ren_scale: typing.SupportsFloat, fact_scale1: typing.SupportsFloat, fact_scale2: typing.SupportsFloat, scale_factor: typing.SupportsFloat = 1.0, custom_scale: madspace._madspace_py.CustomFunction | None = None) -> None

Parameters:

• particle_count – Number of external particles.

• dynamical_scale_type – Scale choice used where a scale is not fixed.

• ren_scale_fixed – Whether the renormalization scale is fixed.

• fact_scale_fixed – Whether the factorization scales are fixed.

• ren_scale – Fixed renormalization-scale value.

• fact_scale1 – Fixed factorization scale for the first beam.

• fact_scale2 – Fixed factorization scale for the second beam.

• scale_factor – Factor on the dynamical scale; fixed scales are left alone.

• custom_scale – Optional user-supplied function that replaces the dynamical scale choice.

class DynamicalScaleType(*args, **kwargs)

Bases: pybind11_object

Members:

transverse_energy

transverse_mass

half_transverse_mass

partonic_energy

Overloaded function.

1. __init__(self: madspace._madspace_py.EnergyScale.DynamicalScaleType, value: typing.SupportsInt) -> None

2. __init__(self: madspace._madspace_py.EnergyScale.DynamicalScaleType, name: str) -> None

half_transverse_mass = <DynamicalScaleType.half_transverse_mass: 2>

EnergyScale.DynamicalScaleType.name -> str

partonic_energy = <DynamicalScaleType.partonic_energy: 3>

transverse_energy = <DynamicalScaleType.transverse_energy: 0>

transverse_mass = <DynamicalScaleType.transverse_mass: 1>

property value

half_transverse_mass = <DynamicalScaleType.half_transverse_mass: 2>

partonic_energy = <DynamicalScaleType.partonic_energy: 3>

transverse_energy = <DynamicalScaleType.transverse_energy: 0>

transverse_mass = <DynamicalScaleType.transverse_mass: 1>